If a US citizen moves to Mexico, can he/she live in a town near the border, maintain his/her coverage of Medicare and come to the US for medical care? He/she would want his medical care to be paid for by Medicare. Would this work?
If you are a US citizen, Medicare will pay for services within the US and its territories. So there should be no problem unless you need emergency care in Mexico because:
Some of the Medigap plans offer travel emergency coverage (80%) but usually only for the first 60 days of a trip. Some pay nothing.
Some Medicare Advantage plans provide coverage benefits for health care costs when traveling outside the United States.
The best advice that I could offer is to contact Medicare and based on what you have (Traditional Medicare? Medigap? Medicare Advantage?), ask what your coverage is.